I've noticed the tires Ihave the most problems with have very thin sidewalls and will crack easily and pick up thorns pretty quickly.
my quads tires are much thicker in those areas, so maybe see if you can find some quad tires in your size to mount.
also use tubes, but that won't help much if the carcass is super thin.
one thing I did on an old sears garden tractor with rotted out side walls was take another tire, slice out the tread and side wall, stick it inside the old tire, then add a tube. it worked for a couple years until I finally found a decent replacement (this was a '60's tractor and odd sized tires).
lastly, if you can't find reasonably thick quad tires, you can get AG tires for mowers. my JDX540 has them and they are awesome. a bit pricey but nice and thick/stiff. I've picked up thorns but not had them puncture, while my old L130's tires were so thin I was constantly plugging them...
oh, and seal the **** out of the bead with bead sealer if you don't use a tube...